The company said the fire is contained to the refinery's property, about 40 miles west of New Orleans, and there have been no injuries.
At least one employee was injured and treated at the scene early Monday, authorities said.
A massive fire at a chemical plant in Illinois continued to burn Tuesday for a second day.
The plume of black smoke slowly disappeared overnight as crews were able to put out the tank fires at the ITC facility in Texas.
Officials said the fire intensified due to temporary reduction of water pressure. Meanwhile, classes resumed for Deer Park and La Porte ISD.